Generating inviscid and viscous fluid-flow simulations over an aircraft surface using a fluid-flow mesh

ABSTRACT

Fluid-flow simulation over a computer-generated aircraft surface is generated using inviscid and viscous simulations. A fluid-flow mesh of fluid cells is obtained. At least one inviscid fluid property for the fluid cells is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. A set of intersecting fluid cells that intersects the aircraft surface are identified. One surface mesh polygon of the surface mesh is identified for each intersecting fluid cell. A boundary-layer prediction point for each identified surface mesh polygon is determined. At least one boundary-layer fluid property for each boundary-layer prediction point is determined using the at least one inviscid fluid property of the corresponding intersecting fluid cell and a boundary-layer simulation that simulates fluid viscous effects. At least one updated fluid property for at least one fluid cell is determined using the at least one boundary-layer fluid property and the inviscid fluid simulation.

BACKGROUND

1. Field

This application relates generally to simulating a fluid flow over anaircraft surface and, more specifically, to generating both inviscid andviscous fluid-flow simulations using a fluid-flow mesh.

2. Description of the Related Art

Aerodynamic analysis of an aircraft moving through a fluid typicallyrequires an accurate prediction of the properties of the fluidsurrounding the aircraft. Accurate aerodynamic analysis is particularlyimportant when designing aircraft surfaces, such as the surfaces of awing or control surface. Typically, the outer surface of a portion ofthe aircraft, such as the surface of a wing, is modeled, eitherphysically or by computer model, so that a simulation of the fluid flowcan be performed and properties of the simulated fluid flow can bemeasured. Fluid-flow properties are used to predict the characteristicsof the wing including lift, drag, boundary-layer velocity profiles, andpressure distribution. The flow properties may also be used to maplaminar and turbulent flow regions near the surface of the wing and topredict the formation of shock waves in transonic and supersonic flow.

A computer-generated simulation can be performed on a computer-generatedaircraft surface to simulate the fluid dynamics of a surrounding fluid.The geometry of the computer-generated aircraft surface is relativelyeasy to change and allows for optimization through design iteration oranalysis of multiple design alternatives. A computer-generatedsimulation can also be used to study situations that may be difficult toreproduce using a physical model, such as supersonic flight conditions.A computer-generated simulation also allows a designer to measure orpredict fluid-flow properties at virtually any point in the model bydirect query, without the difficulties associated with physicalinstrumentation or data acquisition techniques.

In some cases, a computer-generated simulation includes a computationalfluid dynamics (CFD) simulation module used to predict the properties ofthe fluid flow. A CFD simulation module estimates the properties of asimulated fluid flow by applying an algorithm that estimates theinteraction between small simulated fluid volumes, also referred to asfluid cells. Because a single CFD simulation module may include millionsof individual fluid cells, the complexity of the relationship betweenfluid cells can have a large effect on the computational efficiency ofthe simulation. Complex CFD simulation modules can be computationallyexpensive and require hours or even days to execute usinghigh-performance computer processing hardware.

To reduce the computational burden, in some instances it is desirable touse a CFD simulation module that simplifies the fluid dynamics andproduces a fluid simulation that can be solved more rapidly. Forexample, for fluid flows that are relatively uniform or are located awayfrom an aircraft surface, a simplified simulation that minimizes orignores fluid properties that have little effect on the overall behaviorof the fluid can be used. In this way, processing time is improvedwithout sacrificing accuracy or resolution of the final results.

In other situations, where the fluid flow is not as uniform, it may benecessary to use a CFD simulation module that is more sophisticated andcapable of accurately predicting the fluid properties, using morecomplex fluid dynamics. However, more sophisticated simulation modulesare also likely to require more computing resources and thereforerequire more time to solve.

It may be advantageous to construct a hybrid computer-generatedsimulation that employs both a simplified CFD simulation module inlocations where the fluid flow is relatively uniform, and a moresophisticated CFD simulation module in locations where the fluiddynamics are more complex. By combining different CFD simulationmodules, a hybrid computer-generated simulation may increase processingspeed while producing accurate results.

Using multiple CFD simulation modules may be difficult, particularly ifthe CFD simulation modules were not initially designed to work together.The interface between the simulation modules must be constructed so thatthe resulting computer-generated simulation is both computationallyefficient and analytically robust. The techniques described herein solvesome of the difficulties in implementing a computer-generated simulationusing multiple simulation modules.

SUMMARY

One exemplary embodiment includes a computer-implemented method ofgenerating a fluid-flow simulation over a computer-generated aircraftsurface, the computer-generated aircraft surface comprised of a surfacemesh of surface mesh polygons. A fluid-flow mesh is obtained forsimulating a fluid flow over the aircraft surface, the fluid-flow meshcomprising a plurality of fluid cells. At least one inviscid fluidproperty for each of the fluid cells is determined using an inviscidfluid simulation that does not simulate fluid viscous effects. A set ofintersecting fluid cells, of the plurality of fluid cells, thatintersects the aircraft surface is identified. One surface mesh polygonof the surface mesh for each intersecting fluid cell of the set ofintersecting fluid cells is also identified. A boundary-layer predictionpoint for each identified surface mesh polygon is determined. At leastone boundary-layer fluid property for each boundary-layer predictionpoint is determined using the at least one inviscid fluid property ofthe corresponding intersecting fluid cell and a boundary-layersimulation that simulates fluid viscous effects. At least one updatedfluid property is determined for at least one fluid cell of theplurality of fluid cells using the at least one boundary-layer fluidproperty and the inviscid fluid simulation.

DESCRIPTION OF THE FIGURES

FIG. 1 depicts a computer-generated fluid flow applied to acomputer-generated aircraft surface.

FIGS. 2 a and 2 b depict an exemplary fluid flow around a wing surface.

FIG. 3 depicts an exemplary quadrilateral surface mesh and acorresponding structured mesh of the fluid flow.

FIG. 4 depicts an exemplary surface mesh and fluid-flow mesh.

FIG. 5 depicts an exemplary fluid-flow mesh and boundary-layerprediction points.

FIG. 6 depicts a cross-sectional view of an exemplary fluid-flow meshand boundary-layer prediction points.

FIG. 7 depicts a cross-sectional view of an exemplary fluid-flow meshwith partially intersecting fluid cells.

FIG. 8 depicts an exemplary mapping of cells in an exemplary fluid-flowmesh to polygons in an exemplary surface mesh.

FIG. 9 depicts an exemplary schematic diagram for simulating a fluidflow using inviscid and viscous simulation modules.

FIG. 10 depicts an exemplary exchange between the inviscid CFDsimulation module and the boundary-layer CFD module.

FIG. 11 depicts an exemplary computer system for simulating a fluid flowover an aircraft surface.

FIG. 12 depicts an exemplary computer network.

The figures depict one embodiment of the present invention for purposesof illustration only. One skilled in the art will readily recognize fromthe following discussion that alternative embodiments of the structuresand methods illustrated herein can be employed without departing fromthe principles of the invention described herein.

DETAILED DESCRIPTION

As discussed above, a computer-generated simulation can be used toanalyze the aerodynamic performance of a proposed aircraft surface, suchas a wing or control surface. Using known geometry modeling techniques,a computer-generated aircraft surface that represents the outsidesurface of the proposed aircraft can be constructed. FIG. 1 depicts anexemplary computer-generated aircraft surface of the Space Shuttleorbiter vehicle, external tank, and twin solid rocket boosters. A CFDfluid simulation module has been applied using the computer-generatedaircraft surface of the Space Shuttle orbiter to predict the fluidproperties of an exemplary fluid flow.

As shown in FIG. 1, the results of the simulation can be visuallyrepresented as shaded regions on the computer-generated aircraft surfaceof the Space Shuttle. Different shades represent the predicted pressuredistribution resulting from the simulated fluid flow. In FIG. 1,transitions between the shaded regions represent locations of predictedpressure change across the surface of the Space Shuttle. Similarly,different pressures in the surrounding fluid flow are represented asdifferently shaded regions.

In FIG. 1, the simulation of the fluid flow is visualized by depictingthe predicted pressure distribution. However, the simulation may bevisualized using other fluid properties, including surface velocity, airtemperature, air density, and others. Additionally, the simulation maybe used to visualize locations of developing shock waves or transitionsbetween laminar and turbulent flow.

The simulation allows the designer or engineer to evaluate theperformance of the aircraft geometry for various flow conditions. Ifnecessary, changes can be made to the aircraft geometry to optimizeperformance or eliminate an unwanted aerodynamic characteristic. Anothersimulation can be performed using the modified geometry, and the resultscan be compared. To allow for multiple design iterations, it isadvantageous to perform multiple simulations in a short amount of time.However, as described above, there is a tradeoff between speed andaccuracy of the simulation depending on the type of CFD simulationmodule used.

Typically, a computer-generated simulation represents a fluid flow as athree-dimensional fluid-flow mesh of small volumes of fluid called fluidcells. As discussed in more detail below, the shape of the fluid cellscan vary depending on the method used to construct the fluid-flow mesh.A CFD simulation module predicts the interactions between the fluidcells in the fluid-flow mesh, using a fundamental algorithm or fieldequation.

The speed and accuracy of a CFD simulation module depends, in part, onthe field equation used to predict the interaction between the flowcells. In some instances, the field equation simplifies the relationshipbetween flow cells by ignoring or minimizing certain dynamiccontributions. These field equations are typically less complex, andtherefore are more computationally efficient. For instance, a simplifiedalgorithm called the Euler method may be used to simulate a fluid flowwhen viscous effects can be minimized or ignored. Viscous effects of afluid can be ignored when, for example, there is not a significantvelocity difference between adjacent fluid cells, and therefore shearforces due to internal friction or viscosity are minimal. A CFDsimulation module that ignores or minimizes effects of fluid viscositycan also be referred to as an inviscid simulation.

In other instances, a more complex field equation is used to moreaccurately predict the interaction between the flow cells. For example,a Navier-Stokes method can be used to simulate the pressure and shearforces on the flow cells. Unlike the Euler method mentioned above, theNavier-Stokes method accounts for the effects of viscosity and offers amore accurate simulation of a fluid flow. A simulated fluid flow thataccounts for effects due to fluid viscosity can also be referred to as aviscous simulation.

However, the improved accuracy of the Navier-Stokes method comes at thecost of increased computational load, and therefore the Navier-Stokesmethod is generally slower to compute than an Euler-based algorithm.Thus, selecting the field equation for a CFD module often involves atradeoff between speed and accuracy. In practice, designers may usefaster Euler-based CFD models to evaluate multiple design iterations andthen validate the final design iteration with a more accurateNavier-Stokes-based CFD model. However, if the Navier-Stokes CFDsimulation reveals a design problem, the entire process must berepeated, wasting valuable time and computing resources.

The techniques described below are computer-generated simulations thatuse multiple algorithms to achieve acceptable accuracy without requiringthe computational burden of a full Navier-Stokes CFD simulation. In manysimulations, there is a portion of the flow that can be accuratelypredicted without taking viscous contributions into account. Forexample, portions of the fluid flow that are located away from anaircraft surface, such as a wing surface, have a relatively uniformvelocity profile. Therefore, an inviscid simulation using, for example,an Euler-based analysis, can be used to accurately predict the behaviorof these regions of the fluid flow. In other locations of the fluid flowwhere there is a less uniform velocity profile, a more complex, viscoussimulation can be used.

The techniques described herein provide a method of generating asimulation using more than one field equation to simulate the fluid flowover a computer-generated aircraft surface using a fluid-flow mesh andsurface mesh. If the values produced by multiple simulations are notpassed between the meshes by using a one-to-one correlation between meshelements, error and instability may be introduced into the computermodel. Many of these errors may be overcome or greatly reduced byestablishing a one-to-one correlation between, for example, an inviscidfluid-flow mesh element and surface (or boundary-layer) mesh element.The following technique provides one example of how a one-to-onecorrelation can be maintained for computer models using a fluid-flowmesh and a surface mesh that do not align.

The following discussion provides an example of a simulated fluid flowover an aircraft surface, such as a wing surface. However, the techniquemay also be applied to a simulated fluid flow over any type of surfacesubjected to a fluid flow.

1. Simulating Fluid Flow Over a Wing

FIGS. 2 a and 2 b depict a two-dimensional representation of a fluidflow over a wing surface 202 classified by two regions: a free streamregion 204 and a boundary-layer region 206. As shown in FIGS. 2 a and 2b, the boundary-layer region 206 is located near a wing surface 202 andis characterized by a sharply increasing velocity profile 208. Skinfriction causes the fluid very close to the wing surface 202 to beessentially zero, with respect to the surface. A sharply increasingvelocity profile develops as the velocity increases from a near-zerovelocity to the free stream velocity. The sharply increasing velocityprofile 208 in the boundary-layer region 206 creates shear forces withinthe boundary-layer fluid flow. Due to the internal shear forces, viscousproperties of the fluid influence the boundary-layer fluid flow.Therefore, a simulation of the flow in the boundary-layer region 206should account for viscous contributions to the flow dynamics. In somecases, the fluid in boundary-layer region 206 may be characterized asturbulent flow (region 210). Due to fluid voracity, viscous propertiesof the fluid influence the fluid flow. Thus, a simulation of theturbulent flow should also account for viscous contributions to the flowdynamics. For purposes of this discussion, laminar and turbulent regionsare treated as one boundary-layer region and simulated using a singleCFD simulation module.

A CFD simulation module that accounts for viscosity may also be called aviscous CFD simulation module or a boundary-layer CFD simulation module.Below, exemplary field equations for a boundary-layer CFD simulationmodule are provided according to a Drela boundary-layer technique.Drela, M. “XFOIL: An Analysis and Design System for Low Reynolds NumberAirfoils,” pp. 1-12, Proceedings of the Conference on Low ReynoldsNumber Aerodynamics (T. J. Mueller ed., Univ. of Notre Dame, Notre Dame,Ind., 1989).

Equation 1, below, represents a boundary-layer integral momentumequation for compressible flow:

$\begin{matrix}{{{\frac{\theta}{x} + {\left( {2 + H - M_{e}^{2}} \right)\frac{\theta}{u_{e}}\frac{u_{e}}{x}}} = \frac{C_{f}}{2}},} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where θ is the momentum thickness, H is the shape factor, M_(e) is theboundary-layer edge Mach number, u_(e) is the boundary-layer edgevelocity, and C_(f) is the skin friction coefficient.

Equation 2, below, represents a boundary-layer kinetic energy integralequation:

$\begin{matrix}{{{\theta \frac{H^{*}}{x}} + {\left( {{2\; H^{**}} + {H^{*}\left( {1 - H} \right)}} \right)\frac{\theta}{u_{e}}\frac{u_{e}}{x}}} = {{2\; C_{D}} - {H^{*}{\frac{C_{f}}{2}.}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

As used in equations 1 and 2, above, shape factors H, H*, and H** aredefined as:

${H = {{\frac{\delta^{*}}{\theta}H^{*}} = {{\frac{\theta^{*}}{\theta}H^{**}} = \frac{\delta^{**}}{\theta}}}};$

displacement thickness δ* is defined as:

${\delta^{*} = {\int_{o}^{\infty}{\left( {1 - \frac{\rho \; u}{\rho_{e}u_{e}}}\  \right){y}}}};$

momentum thickness θ is defined as:

${\theta = {\int_{o}^{\infty}{\left( {1 - \frac{u}{u_{e}}} \right)\frac{\rho \; u}{\rho_{e}u_{e}}\ {y}}}};$

kinetic energy thickness θ* is defined as:

${\theta^{*} = {\int_{o}^{\infty}{\left( {1 - \left( \frac{u}{u_{e}} \right)^{2}} \right)\frac{\rho \; u}{\rho_{e}u_{e}}\ {y}}}};$

density thickness δ** is defined as:

${\delta^{**} = {\int_{o}^{\infty}{\left( {1 - \frac{\rho}{\rho_{e}}} \right)\frac{u}{u_{e}}\ {y}}}};$

skin friction coefficient C_(f) is defined as:

${C_{f} = \frac{\tau}{\frac{1}{2}\rho_{e}u_{e}^{2}}};$

and dissipation coefficient C_(D) is defined as:

$C_{D} = {\frac{1}{\rho_{e}u_{e}^{3}}{\int_{o}^{\infty}{\tau \frac{\partial u}{\partial y}\ {{y}.}}}}$

Solving equations 1 and 2 for local velocity u and density ρ, theboundary-layer CFD simulation module can predict the fluid propertiesfor portions of the fluid flow within the boundary-layer region 206.Additionally, characteristics of the boundary layer, includingboundary-layer thickness, can also be determined once the fluidproperties are known.

The portions of the fluid flow outside of the boundary-layer region 206may be designated as a free stream region 204. The free stream region204 is typically located away from the wing surface 202. However, thefree stream may be close to the wing surface 202 in areas where theboundary layer is thin or has yet to develop. See, for example, theportion of the fluid flow in FIG. 2 a near the leading edge of the wingsurface 202. The free stream region 204 is usually characterized ashaving a relatively uniform velocity profile 212. When there is auniform velocity profile 212, internal shear forces acting on a fluidmay be relatively small, and therefore viscous contributions to thefluid dynamics can be minimized or ignored.

A CFD simulation module that ignores viscous effects may also be calledan inviscid CFD simulation module. Equation 3, below, provides anexemplary field equation for an inviscid CFD simulation module. Equation3, also called the Euler method, represents the conservation of mass,conservation of three components of momentum, and conservation ofenergy:

$\begin{matrix}{{{\frac{\delta \; m}{\delta \; t} + \frac{\delta \; f_{x}}{\delta \; x} + \frac{\delta \; f_{y}}{\delta \; y} + \frac{\delta \; f_{z}}{\delta \; z}},{{where}\text{:}}}{{m = \begin{pmatrix}\rho \\{\rho \; u} \\{\rho \; v} \\{\rho \; w} \\E\end{pmatrix}};{f_{x} = \begin{pmatrix}{\rho \; u} \\{p + {\rho \; u^{2}}} \\{\rho \; {uv}} \\{\rho \; {uw}} \\{u\left( {E + p} \right)}\end{pmatrix}};{f_{y} = \begin{pmatrix}{\rho \; v} \\{\rho \; {uv}} \\{p + {\rho \; v^{2}}} \\{\rho \; {vw}} \\{v\left( {E + p} \right)}\end{pmatrix}};}{{f_{z} = \begin{pmatrix}{\rho \; w} \\{\rho \; {uw}} \\{\rho \; {vw}} \\{p + {\rho \; w^{2}}} \\{w\left( {E + p} \right)}\end{pmatrix}};}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

where u, v, and w are components of the velocity vector, p is thepressure, ρ is the density, and E is the total energy per unit volume.Combining Equation 3 with an equation of state (e.g., the ideal gaslaw), an inviscid CFD simulation module can predict the fluid propertiesfor the free stream fluid region 204.

2. Combining Multiple CFD Simulation Modules

Using the techniques described below, both the boundary-layer and freestream regions can be simulated by combining viscous and inviscid CFDsimulation modules. For example, FIG. 3 depicts a fluid flow representedas a structured mesh of inviscid fluid cells 302 and a structured meshof boundary-layer fluid cells 304. The mesh of inviscid andboundary-layer fluid cells 302 and 304 are depicted in FIG. 3 in across-sectional representation (two dimensional). Note, however, thatthe fluid cells are actually three-dimensional volumes of fluid.

FIG. 3 also depicts a surface mesh 306 of quadrilateral polygonsrepresenting the surface of a wing. The surface mesh 306 shouldapproximate the curvilinear shape of the wing surface without creatinggaps or breaks between quadrilateral polygons. For relatively simplewing surfaces as shown in FIG. 3, the mesh can be created from multiplewing surface cross-sectional profiles, where each wing profile isapproximated by short line segments. The quadrilateral polygons arecreated by connecting the vertex of each short line segment for adjacentwing profiles.

The structured mesh of inviscid fluid cells 302 shown in FIG. 3 is amesh of fluid volumes defined using a set of vertices of the surfacemesh 306. For a set of four adjacent vertices on the surface mesh 306, avolume 310 is projected from the surface of the wing in a direction asclose to a surface normal as possible. The volume is partitioned intofluid cells 308 by defining at least two surfaces 312 that offset agiven distance from the surface of the wing. The structured meshdepicted in FIG. 3 does not intersect the surface of the wingrepresented by the surface mesh 306.

In FIG. 3, the surface mesh 306, the structured mesh of boundary-layerfluid cells 304, and the structured mesh of inviscid fluid cells 302have been created so that there is a one-to-one correlation to cells atthe mesh boundaries. That is, each mesh element that borders anothermesh corresponds to exactly one cell of the bordering mesh. Therefore,for a given polygon in the surface mesh, there is one correspondingboundary-layer fluid cell, and for that boundary-layer fluid cell thereis one corresponding inviscid fluid cell. This arrangement isadvantageous in that it allows data to be passed from one cell toanother without having to interpolate or estimate the closestneighboring cells.

The construction of the meshes shown in FIG. 3 typically requires thatthe surface mesh 306 of the wing be comprised entirely of quadrilateralpolygons. The structured mesh of boundary-layer fluid cells 304 and thestructured mesh of inviscid fluid cells 302 are then constructed usingthe vertices of the surface mesh 306 as starting points.

There are, however, drawbacks to using this meshing technique. First, itcan be difficult to apply a quadrilateral surface mesh to complexsurface geometries. For example, the segmented-line profile techniquedescribed above does not work for surfaces without a relatively uniformlongitudinal cross section. Also, complex geometries created byintersections between surfaces can be difficult to model using aquadrilateral mesh. For example, a pylon and nacelle hanging off theleading edge of a wing may be difficult to automate and typicallyrequires human interaction or troubleshooting to create a continuous,gap-free surface mesh.

FIG. 4 depicts another technique for creating surface and fluid-flowmeshes. In FIG. 4, the inviscid portion of the fluid flow is representedby a fluid-flow mesh 402, which is depicted as being a Cartesian mesh. ACartesian mesh is defined as a mesh of cube or rectangular cuboid fluidcells 408. That is, each fluid cell 408 is bounded by six flat faceswhere opposite faces are parallel and adjacent faces are orthogonal. Insome cases, larger fluid cells are divided into smaller fluid cells bydefining additional faces at the midpoint of the existing faces. Thus,the fluid cells in a Cartesian mesh can be different sizes. In thepresent exemplary embodiment, because the fluid-flow mesh 402 iscomposed entirely of cube volumes, fluid-flow mesh 402 can beautomatically generated minimizing human interaction andtroubleshooting. Additionally, cube cells tend to produce less errorwhen using CFD simulation techniques due, in part, to the uniformity ofthe mesh cells in multiple mesh directions.

FIG. 4 also depicts a surface mesh 406 that is constructed usingtriangular mesh elements rather than quadrilateral mesh elements.Triangular mesh elements are better suited for representing complexgeometries or intersecting surfaces. This technique is also calledtriangulating the wing surface and can be automated for complexgeometries with little or no human intervention.

Compared to the meshing shown in FIG. 3, the meshing technique depictedin FIG. 4 may be easier to create using automated methods and may resultin a more consistent, continuous mesh. However, using the meshingtechnique depicted in FIG. 4, there is no longer a one-to-onecorrelation between neighboring mesh elements. For example, a givenfluid cell in the fluid-flow mesh of boundary-layer fluid cells 404 nolonger corresponds to a fluid cell in the fluid-flow mesh 402. A givenfluid cell in the fluid-flow mesh of boundary-layer fluid cells 404 alsodoes not correlate to a single surface mesh element on the surface mesh406 of the wing surface. Additionally, for portions of the fluid-flowmesh 402 near the wing surface, there will be at least some fluid cellsthat partially intersect one or more of the triangulated surface meshelements in the surface mesh 406 of the wing surface. Therefore, for anyone bordering cell, there are multiple candidate neighboring cells thatcan be used to exchange data.

Without a one-to-one correlation between cells, passing data between thedifferent mesh elements is more complicated and more prone to error. Forexample, values from one or more bordering inviscid fluid cells may bepassed to a neighboring boundary-layer fluid cell. One or more inviscidfluid cells must be selected and the values interpolated depending onthe degree of overlap between the cells. These techniques tend tointroduce error into the simulation and reduce the robustness of thesolution.

In some cases, the boundary-layer mesh can be derived from theintersection of the fluid-flow mesh 402 and the surface mesh 406. Asshown in FIG. 5, a set of boundary-layer fluid cells may be definedaccording to the location of surface mesh elements with respect to anintersecting plane of fluid cells of the fluid-flow mesh. FIG. 5 depictsa surface mesh 406 of the wing surface intersected by a two-dimensionalstrip 502 representing the centerline of a plane of fluid cells of thefluid-flow mesh. A boundary-layer prediction point 520 is created at theintersection of the strip 502 and the border of each intersected surfacemesh element. The boundary-layer prediction points 520 can be used toconstruct a local boundary-layer fluid-flow mesh with a boundary-layerfluid cell 610 centered on each boundary-layer prediction point 520. Theresulting boundary-layer fluid cells 610 can be used to simulate theboundary-layer portion of the simulated fluid flow. Note that in thisexample, the boundary-layer mesh is one cell thick as viewed along thewing cross-section. See, for example, FIG. 6 depicting boundary-layerfluid cells 610 centered on boundary-layer prediction points 520.

Using the boundary-layer fluid cells 610, a boundary-layer CFDsimulation module can be coupled with an inviscid CFD simulation moduleto predict the fluid property values on and around the wing. In oneexample, an inviscid CFD simulation module determines a local pressure,fluid density, and local velocity values for each fluid cell in thefluid-flow mesh. The boundary-layer CFD simulation module receives fluidproperty values from neighboring inviscid fluid cells. If there is morethan one neighboring inviscid fluid cell present, the boundary-layer CFDmodule typically interpolates the inviscid fluid property values tocombine the results from the multiple neighboring inviscid fluid cells.As discussed above, interpolation techniques may introduce error intothe simulation due to errors in the interpolation and approximating thecontributions from multiple inviscid fluid cells.

Using, for example, equations 1 and 2 above, the boundary-layer CFDmodule determines the properties of the simulated fluid flow in theboundary-layer region. The boundary-layer CFD simulation module returnsfluid properties and/or a transpiration flux value representing afictitious fluid flow into or out of the wing. As mentioned above, theremay be more than one neighboring inviscid fluid cell that receives thesevalues from a corresponding boundary-layer fluid cell. It is also likelythat there is more than one boundary-layer fluid cell neighboring abordering inviscid fluid cell. This mismatch between flow cells maygenerate additional error and/or model instability.

Additional problems may arise because the boundary-layer predictionpoints 520 are not evenly spaced along the two-dimensional strip 502representing the centerline of a plane of fluid cells of the fluid-flowmesh. As shown in FIGS. 5 and 6, boundary-layer fluid cells 610, whichare centered on the boundary-layer prediction points 520, are alsounevenly spaced, resulting in gaps or bunching in the boundary-layerfluid-flow mesh. In fact, the spacing of the boundary-layer fluid cellsis often much finer than the spacing of the inviscid fluid-flow mesh. Inpractice, the mismatched spacing requires numerical smoothing oraveraging to obtain more consistent boundary-layer CFD simulation moduleresults. However, the smoothing can introduce further error in thesimulation and in some cases may produce false or inaccurate predictionsof the fluid behavior.

In summary, because the values produced by each CFD simulation moduleare not passed to a corresponding fluid cell with a one-to-onecorrelation, error and instability are introduced into the computermodel. Error due to interpolation and smoothing also tends to becomeexacerbated as the inviscid and boundary-layer CFD simulation modulesare iterated multiple times.

As suggested above, many of these errors may be overcome or greatlyreduced by establishing a one-to-one correlation between an inviscidfluid cell and a boundary-layer fluid cell. The following techniqueprovides one example of how a one-to-one correlation can be maintainedfor computer models using an inviscid fluid-flow mesh and a surface meshthat do not align.

3. Multiple CFD Simulation Modules with One-to-One Fluid CellCorrelation

FIG. 9 depicts an exemplary process 900 for simulating a fluid flowusing both an inviscid CFD simulation module and a viscous CFDsimulation module. Using the process 900, explained below, a one-to-onecorrelation is determined between the fluid cells used by each CFDsimulation module.

In step 902, a fluid-flow mesh is obtained for simulating the inviscidportion of the fluid flow. In one exemplary embodiment, as shown in FIG.4, the fluid-flow mesh is a Cartesian mesh generated around an aircraftsurface, such as a wing surface. The Cartesian mesh has cube or cuboidfluid cells. Typically, the Cartesian mesh surrounds the aircraftsurface, but it is not necessary to do so.

In step 904, an inviscid CFD simulation module is used to determineinviscid fluid properties for each fluid cell in the fluid-flow mesh.The inviscid CFD simulation module may use the Euler-based method inequation 3 to determine the inviscid fluid properties. The inviscidfluid properties include but are not limited to: local velocity vector,fluid pressure, and fluid density.

In step 906, fluid cells of the fluid-flow mesh that intersect thesurface of the aircraft surface are identified. For example, FIG. 7depicts a cross section of a wing surface (an exemplary aircraftsurface). The cross section depicted in FIG. 7 is taken along the centerof a plane of fluid cells 408 of fluid-flow mesh 402, which is depictedas being a Cartesian mesh. As shown in FIG. 7, some of the fluid cells408 of the fluid-flow mesh 402 intersect the surface of the wing. Fluidcells that at least partially intersect the wing surface are designatedas intersecting fluid cells 710.

While FIG. 7 depicts a cross section of a cut created by theintersection of the plane of fluid cells 408 and the wing surface, asimilar cut can be created using nearly any arbitrary plane thatintersects the wing surface. In some cases, the cut may be defined asthe intersection between a spherical or cylindrical surface and the wingsurface.

In step 908, one representative surface mesh polygon is identified foreach intersecting fluid cell. The representative surface mesh polygonshould be selected based on its proximity to the intersecting fluidcell. FIG. 8 depicts the same set of intersecting fluid cells 710intersecting a surface mesh 406 representing the wing surface shown inFIG. 7. A two-dimensional strip 802 represents the intersection of thecenter of a plane of fluid cells of the fluid-flow mesh and the surfacemesh 406.

In some cases, a centroid 708 of each partially intersecting fluid cell710 is defined. The centroid 708 is the geometric centroid of theportion of the intersecting fluid cell 710 that is outside the wingsurface. A centroid 808 is also defined for nearby surface meshpolygons. A surface mesh polygon having a centroid 808 that is closestto the intersecting fluid cell centroid 708 is selected as therepresentative surface mesh polygon 804. In this example, the centroid808 of the representative surface mesh polygon 804 is associated with apoint on the plane of fluid cells of the fluid-flow mesh intersectingthe surface mesh 406. The associated point for each respective selectedsurface mesh polygon is used as the boundary-layer prediction point 820.

To determine the associated point to be used as the boundary-layerprediction point 820, the intersection of the plane of fluid cells ofthe fluid-flow mesh and the surface mesh may be represented by anintersection line composed of a series of short line segments. Each linesegment represents the intersection between the plane of fluid cells andan intersected surface mesh polygon. The end of each segment fallseither on the edge of an intersecting fluid cell or an intersectedsurface mesh polygon. For a given centroid 808 of a representativesurface mesh polygon 804, a line segment is identified that has amidpoint that is closest to the given centroid 808. This midpoint isthen used as the associated boundary-layer prediction point 820.

A boundary-layer fluid cell 810 may be centered on each boundary-layerprediction point 820. Using this technique, a single boundary-layerfluid cell 810 is selected for each intersecting fluid cell 710. Thus,there is a one-to-one correlation between intersecting inviscid fluidcells and boundary-layer fluid cells, simplifying the data transferbetween the two simulations.

In step 910, at least one boundary-layer fluid property is determinedfor each boundary-layer prediction point 820 or boundary-layer fluidcell 810. The at least one boundary-layer fluid property for aboundary-layer prediction point 820 or boundary-layer fluid cell 810 isdetermined using a viscous or boundary-layer CFD simulation module andthe inviscid fluid properties of the corresponding intersecting fluidcell 710. For example, field equations 1 and 2 described above can beused to determine a momentum thickness using inviscid fluid propertiesof the corresponding intersecting fluid cell 710.

In some cases, the at least one boundary-layer fluid property includes aboundary-layer thickness value and corresponding transpiration fluxvalue. The boundary-layer thickness value represents the distance fromthe surface of the aircraft where the fluid flow can be treated asinviscid. For example, as discussed above, the fluid flow may be treatedas inviscid if the velocity profile of the fluid flow is uniform enoughto ignore the viscosity of the fluid.

A transpiration flux value can also be used to approximate the thicknessof the boundary layer by introducing a fictitious flow of air out of theaircraft surface over an arc length along the boundary-layer stripsolution. The introduction of the fictitious flow modifies the inviscidsimulated flow near the aircraft surface so as to approximate thepresence of a boundary-layer flow having an appropriate thickness. Asthe magnitude of the transpiration flux increases, the fictitious flowincreases, simulating a thicker boundary layer. In some cases, thetranspiration flux can be used to create a fictitious flow of air intothe aircraft surface (negative flux), thereby reducing the thickness ofthe boundary layer.

The transpiration flux can be determined using the output of the Drelaboundary-layer technique described in equations 1 and 2, above. Forexample, the transpiration flow velocity of the transpiration flux canbe determined using:

$\begin{matrix}{{W_{iw} = {\frac{1}{\rho_{iw}}\frac{\;}{s}\left( {\rho_{iw}U_{iw}\delta^{*}} \right)}},} & {{Equation}\mspace{14mu} 4}\end{matrix}$

where ρ_(iw) is the density of the fluid flow at the aircraft surface,U_(iw) is the velocity of the fluid flow at the aircraft surface, δ* isthe computed boundary layer displacement thickness, and s is the arclength along the boundary-layer strip solution. Equation 4 is taken fromLock, R. C., and Williams, B. R., “Viscous-Inviscid Interactions inExternal Aerodynamics,” Prog. Aerospace Sci., Vol. 24, 1987, pp. 51-171.Thus, the transpiration mass flux (density ρ_(iw) times thetranspiration flow velocity W_(iw)) is equal to the rate of change ofthe product of the local density ρ_(iw), local velocity U_(iw), andboundary layer displacement thickness δ* along the solution strip. Afinite difference method can be used to compute the derivative inequation 4. For example, the neighboring solution points along theboundary-layer strip can be used with a second order, backward Lagrangepolynomial formulation to compute the derivatives.

In step 912, at least one fluid property of at least one fluid cell ofthe fluid-flow mesh is updated to account for the changes in theboundary-layer fluid flow. For example, as described above, thetranspiration flux introduces a fictitious fluid flow out of theaircraft surface. An inviscid CFD simulation module can then be used toupdate the fluid properties of the fluid cells of the fluid-flow meshbased on the fictitious fluid flow introduced by the transpiration flux.

FIG. 10 depicts an exemplary exchange between the inviscid CFDsimulation module 1010 and the boundary-layer CFD module 1050. FIG. 10also depicts the operations performed by the CFD module 1010 (i.e.,operations 1012, 1014, 1016) and the boundary-layer CFD module 1050(i.e., operations 1052, 1054, 1056).

As mentioned above, the inviscid CFD simulation module 1010 uses afluid-flow mesh, such as a Cartesian mesh, of fluid cells to representthe volume of fluid around a aircraft surface, such as a wing surface,using a suitable field equation, such as equation 3 above, to predictthe fluid properties for each fluid cell in the fluid-flow mesh. In thisexample, the inviscid CFD simulation module 1010 can be nearly anyexisting Cartesian inviscid flow simulation module.

As described above in reference to FIGS. 7 and 8, a set of intersectingfluid cells are identified that intersect a surface mesh 406representing the aircraft surface. In operation 1012, the inviscid CFDsimulation module 1010 determines at least one inviscid fluid propertyof at least one intersecting fluid cell 710 (FIGS. 7 and 8) of the setof intersecting fluid cells.

In operation 1052, one boundary-layer prediction point 820 (FIG. 8) isdetermined based on the location of the intersecting fluid cell 710(FIG. 8). As described above, for each selected intersecting fluid cell710 (FIG. 8), one representative triangulated surface mesh polygon 804(FIG. 8) is selected based on the proximity of the surface mesh polygon804 (FIG. 8). A point in the representative triangulated surface meshpolygon, such as the centroid 808 (FIG. 8), is then associated with apoint on the plane created by the intersecting fluid cells. Theassociated point can be designated as a boundary-layer prediction point820 (FIG. 8), and can be used to define a boundary-layer fluid cell 810(FIG. 8). Thus, for each intersecting fluid cell, there is onecorresponding boundary-layer fluid cell.

In operation 1014, at least one inviscid fluid property of theintersecting fluid cell 710 (FIG. 8) is passed to the correspondingboundary-layer prediction point 820 (FIG. 8) or boundary-layer fluidcell 810 (FIG. 8). The at least one inviscid fluid property includes,for example, local pressure, fluid density, and local velocity values.

In operation 1054, the boundary-layer CFD simulation module 1050 usesthe at least one inviscid fluid property to predict the at least oneboundary-layer fluid property for the boundary-layer prediction point820 (FIG. 8) or boundary-layer fluid cell 810 (FIG. 8). As describedabove, the boundary-layer CFD module 1050 may use the field equations 1and 2 above to predict one or more boundary-layer fluid properties. Insome cases, the results of the boundary-layer CFD simulation module 1050can then be used to determine a boundary-layer thickness ortranspiration flux value for the boundary-layer prediction point 820(FIG. 8) or boundary-layer fluid cell 810 (FIG. 8).

In operation 1056, one or more boundary-layer fluid properties arepassed to the inviscid simulation module 1010. As described above, insome cases a transpiration flux value is used to introduce a fictitiousflow back into the inviscid fluid-flow cell.

In operation 1016, the inviscid CFD simulation module 1010 uses the oneor more boundary-layer fluid properties to determine at least oneupdated fluid property of at least one fluid cell of the fluid-flowmesh. By updating at least one fluid property of the fluid cell, thefluid-flow simulation accounts for influences due to the boundary-layerflow conditions. In this way, fluid properties (e.g., inviscid fluidproperty and boundary-layer fluid property) can be passed betweeninviscid and boundary-layer CFD simulation modules without requiringinterpolation or smoothing.

Depending on the size of the fluid cells (coarseness of the fluid-flowmesh) and the curvature of the wing surface, the simulation may becomechoppy or stepped and, thus, in some cases, smoothing may be used torefine the results. However, the smoothing is less error inducing thanas described for the techniques above without a one-to-one correlationbetween inviscid fluid cells and boundary-layer fluid cells.

The exemplary exchange between the inviscid CFD simulation module 1010and the boundary-layer CFD module 1050 shown in FIG. 10 is merely anillustrative example. In some cases, modules other than the inviscid CFDsimulation module 1010 and the boundary-layer CFD module 1050 performone or more of the operations described above. In particular,determining the intersecting fluid cell and operation 1052 fordetermining the boundary-layer prediction point may be performed bymodules other than the CFD simulation module 1010 and the boundary-layerCFD module 1050.

Depending on the particular simulation, the process described above maybe iterated several times until a steady-state solution is reached.Thus, the data exchange between the CFD simulation module 1010 and theboundary-layer CFD module 1050 may occur multiple times as thesimulation is iterated.

4. Computer and Computer Network System

The embodiments described herein are typically implemented as computersoftware (computer-executable instructions) executed on a processor of acomputer system. FIG. 11 depicts an exemplary computer system 1100configured to perform any one of the above-described processes. Computersystem 1100 may include the following hardware components: processor1102, data input devices (e.g., keyboard, mouse, keypad) 1104, dataoutput devices (e.g., network connection, data cable) 1106, and userdisplay (e.g., display monitor) 1108. The computer system also includesnon-transitory memory components including random access memory (RAM)1110, hard drive storage 1112, and other computer-readable storage media1114.

Processor 1102 is a computer processor capable of receiving andexecuting computer-executable instructions for performing any of theprocesses described above. Computer system 1100 may include more thanone processor for performing the processes. The computer-executableinstructions may be stored on one or more types of non-transitorystorage media including RAM 1110, hard drive storage 1112, or othercomputer-readable storage media 1114. Other computer-readable storagemedia 1114 include, for example, CD-ROM, DVD, magnetic tape storage,magnetic disk storage, solid-state storage, and the like.

FIG. 12 depicts an exemplary computer network for distributing theprocesses described above to multiple computers at remote locations. Oneor more servers 1210 may be used to perform portions of the processdescribed above. For example, one or more servers 1210 may store andexecute computer-executable instructions for receiving information forgenerating a computer-generated simulation. The one or more servers 1210are specially adapted computer systems that are able receive input frommultiple users in accordance with a web-based interface. The one or moreservers 1210 are able to communicate directly with one another using acomputer network 1220 including a local area network (LAN) or a widearea network (WAN), such as the Internet.

One or more client computer systems 1240 provide an interface to one ormore system users. The client computer systems 1240 are capable ofcommunicating with the one or more servers 1210 over the computernetwork 1220. In some embodiments, the client computer systems 1240 arecapable of running a web browser that interfaces with a web-enabledsystem running on one or mover server machines 1210. The web browser isused for accepting input data from the user and presenting a display tothe user in accordance with the exemplary user interface describedabove. The client computer 1240 includes a computer monitor or otherdisplay device for presenting information to the user. Typically, theclient computer 1240 is a computer system in accordance with thecomputer system 1100 depicted in FIG. 11.

Although the invention has been described in considerable detail withreference to certain embodiments thereof, other embodiments arepossible, as will be understood by those skilled in the art.

1. A computer-implemented method of generating a fluid-flow simulationover a computer-generated aircraft surface, the computer-generatedaircraft surface comprised of a surface mesh of surface mesh polygons,the method comprising: obtaining a fluid-flow mesh for simulating afluid flow over the aircraft surface, the fluid-flow mesh comprising aplurality of fluid cells; determining at least one inviscid fluidproperty for each of the fluid cells using an inviscid fluid simulationthat does not simulate fluid viscous effects; identifying a set ofintersecting fluid cells of the plurality of fluid cells that intersectsthe aircraft surface; identifying one surface mesh polygon of thesurface mesh for each intersecting fluid cell of the set of intersectingfluid cells; determining a boundary-layer prediction point for eachidentified surface mesh polygon; determining at least one boundary-layerfluid property for each boundary-layer prediction point using the atleast one inviscid fluid property of the corresponding intersectingfluid cell and a boundary-layer simulation that simulates fluid viscouseffects; and determining at least one updated fluid property for atleast one fluid cell of the plurality of fluid cells using the at leastone boundary-layer fluid property and the inviscid fluid simulation. 2.The computer-implemented method of claim 1, wherein identifying onesurface mesh polygon for each intersecting fluid cell comprises:obtaining a centroid of an intersecting fluid cell of the set of fluidcells; identifying a surface mesh polygon having a centroid that isclosest to the centroid of the intersecting fluid cell.
 3. Thecomputer-implemented method of claim 2, wherein the centroid of theintersecting fluid cell is the centroid of a region of the intersectingfluid cell that is outside of the aircraft surface.
 4. Thecomputer-implemented method of claim 1, wherein the at least oneboundary-layer fluid property includes a boundary-layer thickness value,the boundary-layer thickness value representing a distance from theaircraft surface where fluid viscous effects can be ignored.
 5. Thecomputer-implemented method of claim 1, wherein the at least oneboundary-layer fluid property includes a transpiration flux value, thetranspiration flux value representing a direction and an amount of fluidflow originating from the aircraft surface.
 6. The computer-implementedmethod of claim 1, wherein the fluid-flow mesh is constructed using aCartesian mesh, wherein the Cartesian mesh comprises: a plurality offlow cells, each flow cell bounded by six flat faces where oppositefaces are parallel and adjacent faces are orthogonal.
 7. Thecomputer-implemented method of claim 1, wherein the inviscid fluidsimulation is an Euler-based flow simulation.
 8. Thecomputer-implemented method of claim 1, wherein the at least oneinviscid fluid property includes a fluid velocity vector, a fluiddensity value, and a fluid pressure value.
 9. The computer-implementedmethod of claim 1, wherein the computer-generated aircraft surface is anairplane wing.
 10. A computer-implemented method of generating afluid-flow simulation over a computer-generated aircraft surface, thecomputer-generated aircraft surface comprised of a surface mesh ofsurface mesh polygons, the method comprising instructions for: obtaininga fluid-flow mesh for simulating a fluid flow over the aircraft surface,the fluid-flow mesh comprising a plurality of fluid cells; determiningat least one inviscid fluid property for each of the fluid cells usingan inviscid fluid simulation that does not simulate fluid viscouseffects; identifying an intersecting fluid cell of the plurality offluid cells that intersects the aircraft surface; determining aboundary-layer prediction point for the intersecting fluid cell;determining at least one boundary-layer fluid property for theboundary-layer prediction point using the at least one inviscid fluidproperty of the intersecting fluid cell; and determining at least oneupdated flow property for at least one fluid cell of the plurality offluid cells using the at least one boundary-layer fluid property and theinviscid fluid simulation.
 11. A non-transitory computer-readablestorage medium comprising computer-executable instructions forgenerating a fluid-flow simulation over a computer-generated aircraftsurface, the computer-generated aircraft surface comprised of a surfacemesh of surface mesh polygons, the instructions comprising instructionsfor: obtaining a fluid-flow mesh for simulating a fluid flow over theaircraft surface, the fluid-flow mesh comprising a plurality of fluidcells; determining at least one inviscid fluid property for each of thefluid cells using an inviscid fluid simulation that does not simulatefluid viscous effects; identifying a set of intersecting fluid cells ofthe plurality of fluid cells that intersects the aircraft surface;identifying one surface mesh polygon of the surface mesh for eachintersecting fluid cell of the set of intersecting fluid cells;determining a boundary-layer prediction point for each identifiedsurface mesh polygon; determining at least one boundary-layer fluidproperty for each boundary-layer prediction point using the at least oneinviscid fluid property of the corresponding intersecting fluid cell anda boundary-layer simulation that simulates fluid viscous effects; anddetermining at least one updated fluid property for at least one fluidcell of the plurality of fluid cells using the at least oneboundary-layer fluid property and the inviscid fluid simulation.
 12. Thecomputer-readable storage medium of claim 11, wherein instructions foridentifying one surface mesh polygon for each intersecting fluid cellcomprises instructions for: obtaining a centroid of an intersectingfluid cell of the set of fluid cells; identifying a surface mesh polygonhaving a centroid that is closest to the centroid of the intersectingfluid cell.
 13. The computer-readable storage medium of claim 12,wherein the centroid of the intersecting fluid cell is the centroid of aregion of the intersecting fluid cell that is outside of the aircraftsurface.
 14. The computer-readable storage medium of claim 11, whereinthe at least one boundary-layer fluid property includes a boundary-layerthickness value, the boundary-layer thickness value representing adistance from the aircraft surface where fluid viscous effects can beignored.
 15. The computer-readable storage medium of claim 11, whereinthe at least one boundary-layer fluid property includes a transpirationflux value, the transpiration flux value representing a direction and anamount of fluid flow originating from the aircraft surface.
 16. Thecomputer-readable storage medium of claim 11, wherein the fluid-flowmesh is constructed using a Cartesian mesh, wherein the Cartesian meshcomprises: a plurality of fluid cells, each fluid cell bounded by sixflat faces where opposite faces are parallel and adjacent faces areorthogonal.
 17. The computer-readable storage medium of claim 11,wherein the inviscid fluid simulation is an Euler-based flow simulation.18. The computer-readable storage medium of claim 11, wherein the atleast one inviscid fluid property includes a fluid velocity vector, afluid density value, and a fluid pressure value.
 19. Thecomputer-readable storage medium of claim 11, wherein thecomputer-generated aircraft surface is an airplane wing.
 20. Anon-transitory computer-readable storage medium comprisingcomputer-executable instructions for generating a fluid-flow simulationover a computer-generated aircraft surface, the computer-generatedaircraft surface comprised of a surface mesh of surface mesh polygons,the instructions comprising instructions for: obtaining a fluid-flowmesh for simulating a fluid flow over the aircraft surface, thefluid-flow mesh comprising a plurality of fluid cells; determining atleast one inviscid fluid property for each of the fluid cells using aninviscid fluid simulation that does not simulate fluid viscous effects;identifying a set of intersecting fluid cells of the plurality of fluidcells that intersects the aircraft surface; identifying one surface meshpolygon of the surface mesh for each intersecting fluid cell of the setof intersecting fluid cells; determining a boundary-layer predictionpoint for each identified surface mesh polygon; determining at least oneboundary-layer fluid property for each boundary-layer prediction pointusing the at least one inviscid fluid property of the correspondingintersecting fluid cell and a boundary-layer simulation that simulatesfluid viscous effects; and determining at least one updated fluidproperty for at least one fluid cell of the plurality of fluid cellsusing the at least one boundary-layer fluid property and the inviscidfluid simulation.